Would you consider most European countries to actually have an effective military deterrent?
By troop count, munitions stock, or the number if tanks and jets I don't see anyone as having a particularly impressive military in Europe. That doesn't mean they couldn't organize one if needed, but that's a different issue.
> Thirdly, America's lack of social services is not due to its powerful military, but due to political choices and inefficiencies.
You're missing a big factor here, cultural differences. America was built on the idea of people making a way for themselves and living or dying by their own successes or failures. We've moved pretty far away from that and do now have social programs and safety nets, smaller than many European countries' nets, but the expectation of making a way for yourself is still under the surface. Many people simply don't want the level of welfare programs seen in other countries.